# How do you solve 8/9=(w-2)/6?

Feb 13, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side by a common denominator for the fractions, in this case $\textcolor{red}{18}$, to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{18} \times \frac{8}{9} = \textcolor{red}{18} \times \frac{w - 2}{6}$

$\cancel{\textcolor{red}{18}} 2 \times \frac{8}{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}}} = \cancel{\textcolor{red}{18}} 3 \times \frac{w - 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}}$

$16 = 3 \left(w - 2\right)$

$16 = \left(3 \times w\right) - \left(3 \times 2\right)$

$16 = 3 w - 6$

Next, add $\textcolor{red}{6}$ to each side of the equation to isolate the $w$ term while keeping the equation balanced:

$16 + \textcolor{red}{6} = 3 w - 6 + \textcolor{red}{6}$

$22 = 3 w - 0$

$22 = 3 w$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $w$ while keeping the equation balanced:

$\frac{22}{\textcolor{red}{3}} = \frac{3 w}{\textcolor{red}{3}}$

$\frac{22}{3} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} w}{\cancel{\textcolor{red}{3}}}$

$\frac{22}{3} = w$

$w = \frac{22}{3}$